• Journal of the military operations research society of Korea
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• v.30 no.1
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• pp.70-80
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• 2004

In discrete red and black, you can stake any amount s in your possession, but the value of s takes positive integer value. Suppose your goal is N and your current fortune is f, with 0＜f＜N. You win back your stake and as much more with probability p and lose your stake with probability, q = 1-p. In this study, we consider optimum strategies for this game with the value of p greater than $\frac{1}{2}$ where the player has the advantage over the house. The optimum strategy at any f when p>$\frac{1}{2}$ is to play timidly, which is to bet 1 all the time. This is called as Timid1 strategy. In this paper, we perform the simulation study to show that the Timid1 strategy is optimum in discrete red and black when p＞\frac{1}{2}.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.439-448
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• 2007

In the paper, we use the theory of normal family to study the problem on entire function that share a finite non-zero value with their derivatives and prove a uniqueness theorem which improve the result of J.P. Wang and H.X. Yi.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.41-57
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• 2000

In this paper, we consider first order generalized difference scheme for the two-point boundary value problem and one-dimensional second order parabolic type problem. The optimal error estimates in $L_p$ and $W^{1,p}$ ($2{\leq}p{\leq}{\infty}$) as well as some superconvergence estimates in $W^{1,p}$ ($2{\leq}p{\leq}{\infty}$) are obtained. The main results in this paper perfect the theory of GDM.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.1
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• pp.157-162
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• 2023

To NP-complete 3-SAT problem, this paper proposes a O(nm) polynomial time algorithm, where n is the number of literals and m is the total frequency of all literals in equation f. The algorithm firstly decides a truth value of a literal in sequence of previously-set priority. The priority order is as follows: a literal whose occurrence in a clause is 1(k=1), a literal which is k≥2 and whose truth value is either 0 or 1, and a literal with the minimum frequency. Then, literals whose truth value is determined are then deleted from clause T and the remaining clauses. This process is repeated l times, the number of literals. As a result, the proposed algorithm has been successful in accurately determining the satisfiability of a given equation f and in deciding the truth value of all the literals. This paper, therefore, provides not only a linear-time algorithm as a viable solution to the SAT problem, but also a basis for solving the P versus NP problem.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.427-435
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• 2008

In this paper we consider the problem of whether certain homogeneous or non-homogeneous differential polynomials in f(z) necessarily have infinitely many zeros. Particularly, this extends a result of Gopalakrishna and Bhoosnurmath [3, Theorem 2] for a general differential polynomial of degree $\bar{d}$(P) and lower degree $\underline{d}$(P).

• Journal of Mechanical Science and Technology
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• v.16 no.5
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• pp.655-665
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• 2002

Two-dimensional elastic analysis of doubly periodic circular holes in an infinite plane is given in this paper. Two cases of loading, remote tension and remote shear, are considered. A rectangular cell is cut from the infinite plane. In both cases, the boundary value problem can be reduced to a complex mixed one. It is found that the eigenfunction expansion variational method is efficient to solve the problem. Based on the deformation response under certain loading, the notched medium could be modeled by an orthotropic medium without holes. Elastic properties for the equivalent orthotropic medium are investigated, and the stress concentration along the hole contour is studied. Finally, numerical examples and results are given.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1167-1170
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• 1993

We look at the problem of defuzzification in situations in which in addition to the usual fuzzy output of the controller there exists some ancillary restriction on the allowable defuzzified values. We provide two basic approaches to address this problem. In the first approach we enforce the restriction by selecting the defuzzified value through a random experiment in which the values which have nonzero probabilities are in the allowable region, this method is based on the RAGE defuzzification procedure and makes use of a nonmonotonic conjunction operator. The second approach which in the spirit of the commonly used methods, a kind of expected value, converts the problem to a constraint optimization problem.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.39-50
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• 2018

In this paper, we deal with the uniqueness problem for the power of p-adic meromorphic functions. The results obtained in this paper are the p-adic analogues and supplements of the theorems given by Yang and Zhang [Non-existence of meromorphic solution of a Fermat type functional equation, Aequationes Math. 76(2008), 140-150], Chen, Chen and Li [Uniqueness of difference operators of meromorphic functions, J. Ineq. Appl. 2012(2012), Art 48], Zhang [Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl. 367(2010), 401-408].

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1297-1314
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• 2019

In this work, we investigate the following fractional boundary value problems $$\{_tD^{\alpha}_T({\mid}_0D^{\alpha}_t(u(t)){\mid}^{p-2}_0D^{\alpha}_tu(t))\\={\nabla}W(t,u(t))+{\lambda}g(t){\mid}u(t){\mid}^{q-2}u(t),\;t{\in}(0,T),\\u(0)=u(T)=0,$$ where ${\nabla}W(t,u)$ is the gradient of W(t, u) at u and $W{\in}C([0,T]{\times}{\mathbb{R}}^n,{\mathbb{R}})$ is homogeneous of degree r, ${\lambda}$ is a positive parameter, $g{\in}C([0,T])$, 1 < r < p < q and ${\frac{1}{p}}<{\alpha}<1$. Using the Fibering map and Nehari manifold, for some positive constant ${\lambda}_0$ such that $0<{\lambda}<{\lambda}_0$, we prove the existence of at least two non-trivial solutions

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.611-622
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• 2023

The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums. Some exact computational formulas are given by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function. A result of W. Peng and T. P. Zhang [12] is extended. The new results avoid the restriction that q is a prime.